When an initial position in a composition is considered good?
What kind of a move makes a good key move in a mate problem?

'Beauty is in the eye of a beholder' or 'Your mileage may vary' are of course two ways to answer,
but still a kind of consensus has arisen between composers and solvers on the above questions.

Concerning the problem position:

* First of all the position must be legal, i.e. achievable from the initial position by legal moves.
* Position should not include unnecessary pieces. For example white officers that do not participate in
mates in any variation are known as "Night wardens" and considered ugly. Having a lot of black pieces is
considered ok, but they should not be added just to make the problem more difficult or complex. The
clarity of the idea in most economical settings is always preferred.
* There should be no promoted pieces on board. However, an exception may be made for pieces, which actually
are promoted, but this fact is discovered only through (simple) retrograde analysis. As an example white
bishop on f3 and white pawns on e2, g2 is acceptable.
* There should be no strong black threat in the position. This would strongly limit the possible
white key moves and give away the solution.

Concerning the key move:

* Of course the key must be unique to avoid cooks.
* Contrary to a game a good key should not use brute force i.e. should not check nor capture opponent's piece.
(A capture of a pawn is considered ok, if it has thematic content)
* A good key seems to create opportunities for the opponent, such as exposing the king to a check, leaving
an important piece open to capture or moving it away from centre of action.
* A good key does not limit the mobility of the opponent's king by taking away an escape square, on the contrary a key that gives new escape squares is considered splendid.
* A good key does not pin important defenders. An unpinning move is an excellent key.

And now that we have created all those fancy guide lines, it is time to see, how to break them Wink .
So, if a strong black threat in the position is unacceptable, surely a problem, where white is in
check to start with must be even worse!
However, see the sample below. Unfortunately I do not have the composer's name. I would be pleased to get source info?

"Unknown", "Some time"

Mate in 2.

And if that was not weird enough, here's an other one from a famous composer.
This time white is in a double check! You can study yourself, what is the point of that?

N.A.MacLeod, 1947 (Dedicated to A.White)

Mate in 2.

Although these two compositions break blatantly the above rules, you should accept these rules as guidelines for your own compositions.
__________________________________There are only three kinds of chessplayers - those who can count and those who cannot....